How do I make a face swap animated character in Blender?
There are multiple ways to do this.

Assuming your three faces share topology, the simplest is to join them as shapekeys to a base version of your mouth, and animate the shapekeys with constant interpolation instead of bezier handles.

If you need to use multiple models, you can control the visibility of a mesh using drivers, driving either Cycles settings or material transparency.  Because Cycles doesn't handle coincident meshes well, even transparent coincident meshes, you may have to combine this with simple shapekeys that shrink the hidden meshes.  Again, you will want to animate with constant interpolation-- you don't want to fade in and out, and you want hard switches.

Your drivers should probably all use the same ultimate control.  A good example would be via a bone, where you set the mix node between a regular shader and a transparency shader based on, say, the global Z position of a particular bone, and you set the expression to be (var>= 1.0) and (var &lt;2.0) .  That way, you make sure that you're never showing two meshes at the same time.